Francisco Facchinei Jong-Shi Pang

离散控制Matlab代码LMI 最优和鲁棒控制中的线性矩阵不等式。 线性矩阵不等式：离散系统-HARISHANKAR PRABHAKARAN。 可以在本书中找到这些LMI ：。 这是一组代码，作为Wikibook中离散时间系统的示例程序（我创建的页面在下面列出，并且相应的MATLAB代码可用）： 要运行这些MATLAB代码，需要YALMIP TOOLBOX和诸如SeDuMi或IBM CPLEX之类的求解器。 A1.m-离散时间Lyapunov稳定性（Caverly 3.1.3） A2.m-离散时间有界实引理（H∞范数）（平均3.2.2） A3.m-离散时间H2规范（平均3.3.2） A4.m-离散时间稳定度（平均3.11.2） A5.m-离散时间可检测性（平均3.12.2） A6.m-离散时间H2最佳全状态反馈控制（平均4.2.2） A7.m-离散时间H2-最佳动态输出反馈控制（平均4.2.4） A8.m-离散时间H∞-最佳全状态反馈控制（平均4.3.2） A9.m-离散时间H∞-最佳动态输出反馈控制（平均4.3.4） A10.m-离散时间混合H2-H∞-最佳全状态反馈控制（平均4.4

This comprehensive book presents a rigorous and state-of-the-art treatment of variational inequalities and complementarity problems in finite dimensions. This class of mathematical programming problems provides a powerful framework for the unified analysis and development of efficient solution algorithms for a wide range of equilibrium problems in economics, engineering, finance, and applied sciences. New research material and recent results, not otherwise easily accessible, are presented in a self-contained and consistent manner. The book is published in two volumes, with the first volume concentrating on the basic theory and the second on iterative algorithms. Both volumes contain abundant exercises and feature extensive bibliographies. Written with a wide range of readers in mind, including graduate students and researchers in applied mathematics, optimization, and operations research as well as computational economists and engineers, this book will be an enduring reference on the subject and provide the foundation for its sustained growth

转自verycd 对制作者表示感谢！ ************************************* 内容简介 本书系统地论述了矩阵论中的各种不等式。全书共分九章，第1章是矩阵论的预备知识；第2～8章分别讨论了有关秩、行列式、特征值、条件数、迹、偏序和受控等方面的不等式；第9章给出了矩阵不等式在线性统计中的几个应用：最后两个附录收集了数量、函数和概率统计中常用的不等式。 本书读者对象为高等院校高年级本科生、研究生、有关专业的教师与数学工作者及工程技术人员。

变分不等式在网络均衡问题中的相关应用（F.GIANNESSI and A.MAUGERI）

Inequalities: Theory of Majorization and Its Applications I Theory of Majorization 1 Introduction 3 A Motivation and Basic Definitions . . . . . . . . . . 3 B Majorization as a Partial Ordering . . . . . . . . . 18 C Order-Preserving Functions . . . . . . . . . . . . . 19 D Various Generalizations of Majorization . . . . . . . 21 2 Doubly Stochastic Matrices 29 A Doubly Stochastic Matrices and Permutation Matrices . . . . . . . . . . . . . . . . . . . . . . . . 29 B Characterization of Majorization Using Doubly StochasticMatrices . . . . . . . . . . . . . . . . . . 32 C Doubly Substochastic Matrices and Weak Majorization . . . . . . . . . . . . . . . . . . . . . . 36 D Doubly Superstochastic Matrices and Weak Majorization . . . . . . . . . . . . . . . . . . . . . . 42 E Orderings on D . . . . . . . . . . . . . . . . . . . . 45 F Proofs of Birkhoff’s Theorem and Refinements . . . 47 G Classes of Doubly Stochastic Matrices . . . . . . . . 52 xvii xviii Contents H More Examples of Doubly Stochastic and Doubly Substochastic Matrices . . . . . . . . . . . . . . . . 61 I Properties of Doubly Stochastic Matrices . . . . . . 67 J Diagonal Equivalence of Nonnegative Matrices . . . 76 3 Schur-Convex Functions 79 A Characterization of Schur-Convex Functions . . . . 80 B Compositions Involving Schur-Convex Functions . . 88 C Some General Classes of Schur-Convex Functions . 91 D Examples I. Sums of Convex Functions . . . . . . . 101 E Examples II. Products of Logarithmically Concave (Convex) Functions . . . . . . . . . . . . . 105 F Examples III. Elementary Symmetric Functions . . 114 G Muirhead’s Theorem . . . . . . . . . . . . . . . . . 120 H Schur-Convex Functions on D and Their Extension to Rn . . . . . . . . . . . . . . . . . . . 132 I Miscellaneous Specific Examples . . . . . . . . . . . 138 J Integral Transformations Preserving Schur-Convexity . . . . . . . . . . . . . . . . . . . . 145 K Physical Interpretations of Inequalities . . . . . . . 153 4 Equivalent Conditions

Linear Matrix Inequalities in System and Control Theory Linear Matrix Inequalities in System and Control Theory Stephen Boyd, Laurent El Ghaoui, E. Feron, and V. Balakrishnan Volume 15 of Studies in Applied Mathematics Society for Industrial and Applied Mathematics (SIAM), 1994 ISBN 0-89871-334-X

通信基础类数学书籍，博士研究生必备书籍。

Linear matrix inequalities in system and control theory

Stephen Boyd关于线性矩阵不等式的经典著作。